Prove each of the following identities:
(cosec θ)(1 + cos θ)(cosec θ – cot θ) = 1
Consider the left – hand side:
L.H.S. = (cosec θ) (1 + cos θ)(cosec θ – cot θ)
= (1 – cos2 θ) × cosec2 θ
(∵ 1 + cot2 θ = cosec2 θ)
= (sin2 θ) × cosec2 θ
(∵ sin2θ + cos2 θ = 1)
= 1
= R.H.S.
Hence, proved.